7T Find the surface of revolution if the curve (t) 3 cos(t), y(t) = 3 sin(t),...
3. Graph the region bounded by the parametric curve x cost and y = et where 0 t Find the length of the curve. b. Find the surface area of revolution when the region is revolved around the y -axis. a.
3. Graph the region bounded by the parametric curve x cost and y = et where 0 t Find the length of the curve. b. Find the surface area of revolution when the region is revolved around the y...
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
Questions 9-11 all deal with the same curve: Consider the curver(t) = (cos(2t), t, sin(2t)) Find the length of the curve from the point wheret = 0 to the point where t = 71 O 75.7 G O 7/3.7 2. O 7V2.7 2 7.T 2 3 (Recall questions 9-11 all ask about the same curve) Find the arc-length parametrization of the curver(t) = (cos(26), t, sin(2t)), measure fromt O in the direction increasing t. Or(s) = (cos(V28), V28, sin(28)) Or(s)...
Consider the surface z = f(x, y) = sin(x) + cos(y) and the curve C in the xy plane defined parametrically as x(t) = 2cos(t), y(t) = sin(t) a. Find z'(t). Imagine you are walking directly above the curve C in the direction of increasing t. Find the values of t for which you are walking uphill. Hint:Graph z'(t). Graph f(x, y) for -7 < x < 7 and -7 < y < 7. (You will have to find software...
1. The unbounded plan ar region bet ween the z-axis and the curve yis revolved about the r2 1 T-axis (a) Find the volume of the resulting solid of revolution b) Does the solid have faite surface area? Justify sour answer carefilly
1. The unbounded plan ar region bet ween the z-axis and the curve yis revolved about the r2 1 T-axis (a) Find the volume of the resulting solid of revolution b) Does the solid have faite surface area?...
#43 and #47 please
Surface Area - Surfaces of Revolution In Exercises 43–70, a curve C with parametrization = X(t), y=0, z = 2(t), for t in (a, b), is revolved about the z-axis to create a surface S. Find the surface area A of S. NOTE: Only the first four prob- lems are like Example 13.2.7 (a) and you will have to use integrals over two subintervals of [a, b] to compute A. 13. X = t3 – įt,...
Let S be the ‘football’ surface formed by rotating the curve y =
0, x = cos z for z ∈ [−π/2, π/2], around the z-axis. Find a
parametrization for S, and compute its surface area. Please answer
in full With full instructions.
Let S be the 'football, surface formed by rotating the curve y = 0, x-cosz for-E-π/2, π/2], around the z-axis. Find a parametrization for S, and compute its surface area 3
Let S be the 'football, surface...
2. A dragon is flying around in a pattern given by the parametric curve r(t) (cos(t) cos((sin(t) sin(t) cos(t)j. cos(t) - cos sin(t)-sin(t) cos(t))j (a) Find a formula for the velocity of the dragon at time t (b) Find all the times at which the dragon's speed is zero. Explain your reasoning. c) Does the path of the dragon contain any cusps? Explain your reasoning
2. A dragon is flying around in a pattern given by the parametric curve r(t)...
T Find the length of the curve e' cos(t) e' sin(t) for 0 < t < 2 y (Hint: You can simplify the integrand by expanding the argument inside the square root and applying the Pythagorean identity, sinº (0) + cos²O) = 1.)
Find the surface area of the solid of revolution obtained by
rotating the curve
x=(1/12)(y^2+8)^(3/2)
from ?=2 to ?=5 about the x-axis:
(1 point) Find the surface area of the solid of revolution obtained by rotating the curve X= +8)3/2 from y = 2 to y = 5 about the x-axis: